Space2Num: Vision-to-Number Spatial Reasoning

• Space2Num is a vision-to-number task within the SpaceNum benchmark that maps visual observations to precise numerical outputs capturing spatial changes and layouts.
• The benchmark employs multiple-choice tasks to evaluate metric grounding by testing VLMs on inferring movement magnitudes and object coordinates from visual inputs.
• Empirical findings reveal generally low performance across models, underscoring challenges in achieving reliable numerical calibration and the need for enhanced spatial reasoning modules.

to=arxiv_search 大发彩票官网 彩神争霸官网 天天彩票软件િક्शन ചികിത്സ code: {"query":"(Zhang et al., 22 May 2026) SPACENUM Revisiting Spatial Numerical Understanding in VLMs", "max_results": 5} to=search_arxiv мәҗбурണ Space2Num is the vision-to-number component of the SpaceNum benchmark introduced in "SPACENUM: Revisiting Spatial Numerical Understanding in VLMs" (Zhang et al., 22 May 2026). It comprises tasks in which a vision-LLM (VLM) is given visual observations and must infer the numerical quantities that explain a spatial transition or a static spatial arrangement, such as action magnitudes, object coordinates, or size-related values. Within the benchmark, Space2Num is designed to test whether numerical outputs are metrically grounded in visual spatial structure rather than merely plausible at the language level, and it is studied in two settings: numbers as dynamic transitions during exploration, and numbers as static layouts in spatial reasoning (Zhang et al., 22 May 2026).

1. Conceptual position within the SpaceNum framework

SpaceNum separates two ways in which numbers arise in spatial problems. In the dynamic setting, numbers parametrize changes in an agent’s state, as in action magnitudes for movement or rotation. In the static setting, numbers encode a scene’s spatial structure, as in coordinates of a target object relative to anchors. Space2Num is the direction from vision-side space to language-side numbers: given what is seen, infer the numbers that best describe it.

This role is complementary to Num2Space, which asks for the reverse mapping from numbers to visual outcomes. The distinction is not merely formal. Space2Num probes whether a model can encode observed geometry back into calibrated numerical form, whereas Num2Space probes whether a model can interpret a numerical specification as a plausible spatial consequence. The benchmark treats these as separate competencies rather than assuming bidirectional equivalence (Zhang et al., 22 May 2026).

A central premise of Space2Num is that numerically expressed outputs in embodied or spatial tasks should carry metric content. In this sense, “grounding” means that the inferred number corresponds to a property derivable from the observation itself: meters moved, degrees rotated, coordinates under a specified reference system, or object size in a consistent unit. The benchmark is therefore aimed at metric spatial grounding rather than generic scene description.

2. Formal task structure and variants

Space2Num has two principal instantiations.

Setting	Input	Required output
Dynamic transitions	Two observations $o_t, o_{t+1}$ and an action type $a$	The numerical magnitude $n$ of the action
Static layouts	One observation $o$ under an anchor-defined reference frame	The numerical coordinates $\mathbf{p}$ of a target object

In the dynamic variant, the model is given an initial image, a next image, and a known action type such as Move Forward or Rotate Left. It must infer the numerical magnitude that transforms $o_t$ into $o_{t+1}$. The benchmark implements this as multiple choice: the model receives several candidate magnitudes and must output only the option letter corresponding to the correct one. The task therefore evaluates the ability to map relative visual change to a discrete numerical label (Zhang et al., 22 May 2026).

In the static-layout variant, the model is given a single scene image together with a reference coordinate system defined by two anchor objects. One anchor sets the origin, and the vector between the two anchors defines a direction; this removes ambiguity in the coordinate frame. The model must infer the numerical coordinates of a specified target object under that frame. The benchmark again uses multiple choice, with distractor tuples that differ in position and, in some cases, size (Zhang et al., 22 May 2026).

The dynamic transition setting spans four motion families: Move F/B, Move L/R, Rotate L/R, and Rotate U/D. The allowed magnitude ranges are discrete: Move F/B uses 0.2–2.4 m with step 0.2 m; Move L/R uses 0.2–1.2 m with step 0.2 m; Rotate U/D uses 10–70° with step 10°; and Rotate L/R uses 10–70° with step 10°. The static-layout setting is partitioned into six subtasks: 1D-Map-D, 2D-Map-D, 3D-Map-D, 1D-Map-R, 2D-Map-R, and 3D-Map-R, where D denotes desktop-scale and R denotes room-scale scenes.

The main evaluation metric is multiple-choice accuracy,

$$\text{Accuracy} = \frac{\# \text{correct predictions}}{\# \text{questions}}.$$

For dynamic transitions, the paper also introduces a proximity score for analysis, assigning $\{100, 70, 40, 0\}$ to exact, near, moderate, and far errors according to numerical distance, but this is not the primary benchmark metric (Zhang et al., 22 May 2026).

3. Benchmark construction and data generation

The dynamic Space2Num dataset is built in AI2-THOR. An embodied agent is placed in indoor scenes, an initial valid state is sampled, a primitive action with a sampled magnitude is executed, and the pre-action and post-action images are recorded. Dataset construction is governed by three explicit constraints: transition continuity, visual anchoring, and data validity. Transition continuity ensures that consecutive observations overlap enough to remain visually related while still expressing meaningful spatial change. Visual anchoring discards frames with fewer than 3 object instances. Data validity uses occupancy maps to ensure that sampled actions are valid and do not create collisions or empty frames (Zhang et al., 22 May 2026).

Each dynamic sample therefore contains a pair of images, a known action type, a hidden true magnitude, and a multiple-choice candidate set. Figure 1 reports, for example, “Move F/B: 100/1920” under Space2Num, interpreted there as 100 test samples and 1920 training samples for that action type. The dynamic Space2Num test set contains 400 questions in total, and the paper also reports an automatically generated training corpus of approximately 77,412 training samples overall across tasks for tuning experiments (Zhang et al., 22 May 2026).

The static-layout dataset is built in NVIDIA Isaac Sim with BlenderKit assets. Two anchors define the coordinate system; a third object serves as the target; and layouts are generated under non-overlap and reasonable-distance constraints. The benchmark varies position only, size only, or both position and size. It also varies scene scale between desktop-scale and room-scale, and it represents the same underlying layouts at 1D, 2D, or 3D levels of spatial completeness (Zhang et al., 22 May 2026).

For the static Space2Num benchmark, the simulator provides exact object states, from which the target object’s position in the defined coordinate system and, in some settings, size-related information are taken as the numerical ground truth. The static Space2Num test set contains 1500 questions. Together with the corresponding Num2Space tasks, the full benchmark comprises 3,800 test question-answer pairs (Zhang et al., 22 May 2026).

4. Models, prompting, and measurement protocol

The benchmark evaluates 18 VLMs from 6 families, spanning 2B to 72B parameters: Qwen2.5-VL, Qwen3-VL, InternVL3.5, Gemma-3, Ovis2.5, and Cosmos-Reason2. The reported model variants are Qwen2.5-VL 3B, 7B, 32B, 72B; Qwen3-VL 4B, 8B, 32B; InternVL3.5 4B, 8B, 14B, 38B; Gemma-3 4B, 12B, 27B; Ovis2.5 2B, 9B; and Cosmos-Reason2 2B, 8B (Zhang et al., 22 May 2026).

All Space2Num tasks are presented as multiple-choice problems. The models are explicitly instructed to output only the option letter and not an explanation. Base evaluation uses instruction-following or zero-shot inference without fine-tuning. The reported inference settings are temperature 0.7, top-p 0.9, top-k 50, and bfloat16 with Flash Attention 2. In separate “think” versus “non-think” experiments, reasoning-style outputs are enabled, but evaluation still reduces predictions to the final option letter (Zhang et al., 22 May 2026).

Random baselines depend on the number of options. For 4-option tasks, random guess accuracy is 25%. The paper also uses 30% as a convenient average random baseline in some aggregated dynamic-transition views. For static layouts, additional analysis decomposes errors into “Position Wrong,” “Size Wrong,” and “Position+Size Wrong,” allowing the paper to distinguish localized failures from failures of whole-layout reconstruction (Zhang et al., 22 May 2026).

Methodologically, Space2Num is not framed as a regression benchmark. The emphasis is on discrimination among plausible but distinct numeric candidates under controlled visual conditions. This design makes it possible to compare dynamic and static settings, model families, reasoning modes, and interventions under a common evaluation regime.

5. Empirical findings and directional asymmetries

Across all Space2Num subtasks, the benchmark reports generally weak performance. The strongest models, including Qwen2.5-VL-72B and InternVL3.5-38B, reach only around the high 30s or low 40s percent on average across Space2Num subtasks. Many smaller models are close to or below the random baseline (Zhang et al., 22 May 2026).

In dynamic transitions, the best models reach around 40% accuracy versus an approximately 30% random baseline in the aggregated presentation. Performance remains consistently low across Move F/B, Move L/R, Rotate L/R, and Rotate U/D, without a strong preference for translational over rotational families. In static layouts, the difficulty increases sharply with scene scale and dimensionality: 1D desktop layouts can reach 60–70% accuracy for top models, whereas 3D room layouts are often near or just above 25%, effectively chance-level for 4-way selection (Zhang et al., 22 May 2026).

A major result is directional asymmetry between Space2Num and Num2Space. In dynamic transitions, models generally do better on Space2Num than on Num2Space: inferring a motion magnitude from two images is easier than selecting the correct future observation from an action-plus-number description. In static layouts, the asymmetry reverses: models do better on Num2Space than on Space2Num, suggesting that projecting numbers into a plausible scene is easier than recovering structured numeric layout from a raw image (Zhang et al., 22 May 2026).

Some Space2Num subtasks even produce below-random performance for some models. The paper uses this not as a sign of mere noise but as evidence that current VLMs do not reliably ground numerical values in spatial meaning. A plausible implication is that performance reflects reliance on unstable priors or superficial visual correlations rather than calibrated metric reasoning.

6. Failure modes, reasoning traces, and diagnostic interventions

The paper’s error analysis distinguishes exact failure from near-miss behavior. In dynamic Space2Num, larger models are often numerically less wrong when they fail: proximity scores rise with model size, meaning wrong answers tend to be closer to the true magnitude. Exact-match accuracy, however, remains low. This indicates partial sensitivity to scale without reliable calibration to the correct discrete value (Zhang et al., 22 May 2026).

The dynamic benchmark also tests rotational symmetry, such as equivalences between rotate-left by $20^\circ$ and rotate-right by $a$0. Accuracy drops substantially under these equivalence transformations. This is presented as evidence of a lack of geometric consistency in the mapping from observed visual change to numerical representation (Zhang et al., 22 May 2026).

For static layouts, error decomposition shows that failures are dominated by “Position+Size Wrong” rather than isolated position-only or size-only mistakes. The paper interprets this as evidence that models often fail to construct the whole layout correctly rather than making a small attribute-specific error. This suggests coarse holistic matching rather than disentangled spatial reasoning (Zhang et al., 22 May 2026).

Reasoning-trace analysis identifies three recurrent failure patterns. First, models often stop at coarse spatial cues: for example, noticing that a new object becomes visible or that one object lies left of another, but not performing the fine-grained metric comparison needed to distinguish candidate magnitudes or coordinate tuples. Second, they often fail to reason counterfactually about motion magnitude, treating any noticeable change as support for a large motion even when stable visual evidence rules that out. Third, they frequently reason in image space rather than in the anchor-defined coordinate system, mapping image-left directly to smaller $a$1 or inferring depth without reorienting to the task’s reference frame (Zhang et al., 22 May 2026).

Controlled interventions reinforce these diagnoses. Adding explicit visual anchors in dynamic transitions yields only minor and inconsistent changes, often within $a$2–$a$3 accuracy. Reducing clutter in static layouts by removing irrelevant objects yields only tiny gains, below $a$4–$a$5 on average. Changing numeric surface form, such as using natural language (“one meter”) instead of symbolic notation, produces negligible gains; integer-scaled units yield only slight improvements for dynamic tasks in larger models. By contrast, replacing rendered scenes with structured abstractions such as points, 2D boxes, or 3D boxes substantially improves Space2Num accuracy. This suggests that a primary bottleneck lies in transforming raw visual observations into structured spatial representations rather than in mapping explicit geometric structure to numbers (Zhang et al., 22 May 2026).

7. Tuning results, transfer, and broader significance

The paper reports two main tuning regimes on Qwen3-VL models. The first is supervised tuning with LoRA on Qwen3-VL 4B and 8B, using LoRA rank 8, alpha 16, learning rate $a$6, cosine decay, 10% warmup, bfloat16, maximum sequence length 2048, batch size 128, and 3 epochs. Training uses 77,412 SPACENUM samples with varying mixes of dynamic and static tasks. The reported effect is dimension-specific improvement: tuning on 1D layouts most strongly improves 1D Space2Num, with limited but nonzero transfer to 2D and 3D. The best overall spatial numerical ability is obtained when training data is approximately 25% dynamic transitions and 75% layouts, with larger data volume generally improving performance (Zhang et al., 22 May 2026).

The second regime is GRPO-based reinforcement learning on Qwen3-VL-4B with LoRA rank 64, alpha 64, learning rate $a$7, rollout batch size 128, actor batch size 64, and 5 rollouts per prompt. Two reward designs are compared: strict exact-match reward and graded reward proportional to numerical closeness. Reported improvements over the base model are as follows: Transition tasks, +6.38 under strict reward and +6.88 under graded reward; Layout tasks, +6.64 and +7.60; Num2Space, +8.10 and +9.37; Space2Num, +5.05 and +5.52. Graded reward slightly outperforms strict reward, especially for dynamic Space2Num (Zhang et al., 22 May 2026).

These gains partially transfer to external spatial reasoning benchmarks. After SPACENUM tuning, OmniSpatial Motion improves by +5.5 points for 4B and +4.5 for 8B; SAT-AC improves by +8.1 for 4B and +18.9 for 8B; SAT-OM improves by +43.5 for 4B and +34.8 for 8B. This suggests that improvements in Space2Num and Num2Space are not entirely benchmark-local and can generalize to action-consequence and motion-reasoning settings (Zhang et al., 22 May 2026).

In embodied and robotic contexts, Space2Num is directly analogous to the perception-to-action-parameterization stage: deriving a movement magnitude, rotation, or coordinate target from visual input. The benchmark therefore has immediate implications for safety, robustness, and reliability. Incorrect inferred magnitudes can cause collisions or unsafe motion; poor invariance under equivalent transformations can yield inconsistent behavior; and dependence on shallow cues implies fragility across environments. The paper’s broader conclusion is that present-day VLMs often do not reliably map visual observations to numerically correct spatial descriptions, even when those descriptions appear linguistically well formed. This suggests that deployment in numerically grounded embodied settings requires more explicit spatial modules, stronger spatial abstraction mechanisms, or specialized training beyond generic VLM pretraining (Zhang et al., 22 May 2026).